The regime of Col. Moammar Gadhafi is over in Libya, President Barack Obama said Monday.

In a taped statement Monday afternoon from Martha's Vineyard, Mass., where he has been monitoring developments while on vacation, Obama acknowledged that fighting continued amid a "fluid and uncertain" atmosphere in Tripoli and other major parts of Libya.

But "the situation in Libya has reached a tipping point," he said, and the U.S. stands ready to help opposition leaders rebuild the country.

"This much is clear: The Gadhafi regime is coming to an end," Obama said, "The future of Libya is in the hands of its people."

Repeating comments he made in a written statement Sunday night, Obama said the U.S. recognized the opposition's National Transitional Council as the government of Libya and would be its "friend and partner."

As rebels claimed to control of most of the Libyan capital, it still wasn't clear Monday where Gadhafi was.

U.S. intelligence believes he could still be dug in somewhere in or near Tripoli, U.S. officials told NBC News, and Obama said he "still has the opportunity to relinquish power and lay down arms for sake of Libya."

Obama made a point of calling on the opposition "to take steps to ensure a peaceful transition" and said "the rights of all Libyans must be respected."

The comments came as the rebels' leader warned that some opposition forces were breaking off on their own and ignoring the chain of command. He called on them to follow orders from Benghazi, the rebel headquarters, and said that if they didn't, he could resign.

U.S. officials told NBC News that the U.S. believed Gadhafi hadn't fled the country, unlike other senior figures. A variety of sources have reported that he was headed for any of several countries, among them Venezuela, Algeria and Chad, but the U.S. officials said they had no confirmation that he had even been invited by a foreign country.

U.S. intelligence agencies believe Gadhafi could still be hiding somewhere in Libya, most likely in the Tripoli area, a senior official at the Defense Department said Monday.Video: Libyan rebels control ‘almost all of Tripoli’ (on this page)

Rep. Mike Rogers, R-Mich., chairman of the Intelligence Committee, agreed, saying in an interview with MSNBC TV, "I believe he is in a bunker or a secure situation in Tripoli."

Arabic television reported Sunday night that Gadhafi had been spotted overnight in Tripoli but fought off rebel attempts to capture him.

Nacua, the rebel diplomat, said opposition fighters would "turn over every stone to find him, to arrest him and to put him in the court."

Gadhafi, 69, urged civilians to take up arms against rebel "rats." He said in an audio broadcast that he was in the city and would be "with you until the end," but there was little sign of popular opposition to the rebel offensive.Video: Gadhafi rule crumbles as rebels surge (on this page)

Three of Gadhafi's sons — Saif, Mohammed and, most recently, according to reports, Saadi — were captured by the rebels, but Al Jazeera reported that Mohammed Gadhafi managed to escape Monday.

Get the latest updates from Breakingnews.com

NATO promised to maintain its air campaign until all pro-Gadhafi forces surrendered or returned to barracks. NATO warplanes have hit at least 40 targets in and around Tripoli in the last two days — the highest number on a single geographic location since the bombing started more than five months ago, the alliance said.Interactive: Libyan uprising (on this page)

The U.S., which is part of the NATO campaign, will continue flying Predator drone missions — some of them armed — over Libya, the Defense Department official told NBC News. But for now, the Obama administration's policy that there would be no "U.S. boots on the ground" remains in effect, the official said.

'We still don't believe that this is happening'Some warned of a risk of a longer, anarchic civil war after what has been the bloodiest of the Arab Spring uprisings inspired by the overthrow of autocrats in Tunisia and Egypt. Mustafa Abdel-Jalil, head of the opposition's National Transitional Council, insisted that "the real moment of victory" wouldn't come until Gadhafi was captured.

At a news conference in the rebels' headquarters city, Benghazi, Abdel-Jalil promised a fair trial for Gadhafi and called for civilians and of public and private property to be protected.

Abdel-Jalil expressed deep frustration with indiscipline within the rebel movement, warning that some fighters' refusal to observe the chain of command "might be the reason or the cause of my resignation."Story: With Gadhafi out of power, oil prices should fall

But residents of major Libyan cities were still celebrating the apparent fall of Gadhafi.

The regime of Col. Moammar Gadhafi is over in Libya, President Barack Obama said Monday.

In a taped statement Monday afternoon from Martha's Vineyard, Mass., where he has been monitoring developments while on vacation, Obama acknowledged that fighting continued amid a "fluid and uncertain" atmosphere in Tripoli and other major parts of Libya.

But "the situation in Libya has reached a tipping point," he said, and the U.S. stands ready to help opposition leaders rebuild the country.

"This much is clear: The Gadhafi regime is coming to an end," Obama said, "The future of Libya is in the hands of its people."

Repeating comments he made in a written statement Sunday night, Obama said the U.S. recognized the opposition's National Transitional Council as the government of Libya and would be its "friend and partner."

As rebels claimed to control of most of the Libyan capital, it still wasn't clear Monday where Gadhafi was.

U.S. intelligence believes he could still be dug in somewhere in or near Tripoli, U.S. officials told NBC News, and Obama said he "still has the opportunity to relinquish power and lay down arms for sake of Libya."

Obama made a point of calling on the opposition "to take steps to ensure a peaceful transition" and said "the rights of all Libyans must be respected."

The comments came as the rebels' leader warned that some opposition forces were breaking off on their own and ignoring the chain of command. He called on them to follow orders from Benghazi, the rebel headquarters, and said that if they didn't, he could resign.

U.S. officials told NBC News that the U.S. believed Gadhafi hadn't fled the country, unlike other senior figures. A variety of sources have reported that he was headed for any of several countries, among them Venezuela, Algeria and Chad, but the U.S. officials said they had no confirmation that he had even been invited by a foreign country.

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U.S. intelligence agencies believe Gadhafi could still be hiding somewhere in Libya, most likely in the Tripoli area, a senior official at the Defense Department said Monday.Video: Libyan rebels control ‘almost all of Tripoli’ (on this page)

Rep. Mike Rogers, R-Mich., chairman of the Intelligence Committee, agreed, saying in an interview with MSNBC TV, "I believe he is in a bunker or a secure situation in Tripoli."

Arabic television reported Sunday night that Gadhafi had been spotted overnight in Tripoli but fought off rebel attempts to capture him.

Nacua, the rebel diplomat, said opposition fighters would "turn over every stone to find him, to arrest him and to put him in the court."

Gadhafi, 69, urged civilians to take up arms against rebel "rats." He said in an audio broadcast that he was in the city and would be "with you until the end," but there was little sign of popular opposition to the rebel offensive.Video: Gadhafi rule crumbles as rebels surge (on this page)

Three of Gadhafi's sons — Saif, Mohammed and, most recently, according to reports, Saadi — were captured by the rebels, but Al Jazeera reported that Mohammed Gadhafi managed to escape Monday.

Get the latest updates from Breakingnews.com

NATO promised to maintain its air campaign until all pro-Gadhafi forces surrendered or returned to barracks. NATO warplanes have hit at least 40 targets in and around Tripoli in the last two days — the highest number on a single geographic location since the bombing started more than five months ago, the alliance said.Interactive: Libyan uprising (on this page)

The U.S., which is part of the NATO campaign, will continue flying Predator drone missions — some of them armed — over Libya, the Defense Department official told NBC News. But for now, the Obama administration's policy that there would be no "U.S. boots on the ground" remains in effect, the official said.

'We still don't believe that this is happening'Some warned of a risk of a longer, anarchic civil war after what has been the bloodiest of the Arab Spring uprisings inspired by the overthrow of autocrats in Tunisia and Egypt. Mustafa Abdel-Jalil, head of the opposition's National Transitional Council, insisted that "the real moment of victory" wouldn't come until Gadhafi was captured.

At a news conference in the rebels' headquarters city, Benghazi, Abdel-Jalil promised a fair trial for Gadhafi and called for civilians and of public and private property to be protected.

Abdel-Jalil expressed deep frustration with indiscipline within the rebel movement, warning that some fighters' refusal to observe the chain of command "might be the reason or the cause of my resignation."Story: With Gadhafi out of power, oil prices should fall